A transference theorem for the Dunkl transform and its applications

作者：Dai, Feng^*; Wang, Heping

来源：Journal of Functional Analysis, 2010, 258(12): 4052-4074.

DOI：10.1016/j.jfa.2010.03.006

• Hormander type multiplier theorem
• Dunkl transform
• Transference theorem
• h-Harmonics

For a family of weight functions invariant under a finite reflection group, we show how weighted L(p) multiplier theorems for Dunkl transform on the Euclidean space R(d) can be transferred from the corresponding results for h-harmonic expansions on the unit sphere S(d) of R(d+1) The result is then applied to establish a Hormander type multiplier theorem for the Dunkl transform and to show the convergence of the Bochner-Riesz means of the Dunkl transform of order above the critical index in weighted L(p) spaces.

• 出版日期2010-6-15
• 单位首都师范大学